It is noted that the representation theorem in learning theory
[1]} implies that the generalization capability of
an optimal learning algorithm in SDHS is not worse than that of
learning in RKHS with convex loss function. Corollary REF 
then shows that if \(f_\rho \in W_2^r\) , then the generalization
capability of an optimal learning scheme in SDHS associated with
\(L_{2n}\)  is not worse than that of any optimal learning algorithms
in the corresponding RKHS. More specifically, () shows that as far as the learning rate is concerned, all
\(l^q\)  regularization schemes (REF ) for \(0< q<\infty \) 
can realize the same almost optimal theoretical rate. That is to
say, the choice of \(q\)  has no influence on the generalization
capability of the learning schemes (REF ). This also
gives an affirmative answer to Problem 1 in the sense of
expectation. Here, we emphasize that the independence of
generalization of \(l^q\)  regularization on \(q\)  is based on the
understanding of attaining the same almost optimal generalization
error. Thus, in application, \(q\)  can be arbitrarily specified, or
specified merely by other no generalization criteria (like
complexity, sparsity, etc.).
